Some things that confuse me in Maths.?

Question

First, when a question involves f(x) e.g

f(x) = x² + 2x + 5

Why do we use f(x) over, say Y? Or, inother words what advantage does f(x) give over y. In these two equations, does having a Y instead of F(x) change anything?

f(x) = x² + 2x + 5

y = x² + 2x + 5

Does the f represent the ², co-efficient 2, and +5?

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Next, in the following equation what do you do first? Square or multiply:

2(x+3)²

Inother words does it equal (2x + 3)² or 2(x² + 6x + 9)

[I knew this before, but i've completely forgotten. I think you do the indicies first but i'm not sure]

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Finally, when completeing the square, why do we divide the coefficient of x by 2?

Thanks!

Answer 1

f(x) =y　　　function (x) =y

it means, function that takes x as an unknown quantity.

and for simplicity, we use y , that's all

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do first square or multiply?

it depends.

If it is  2 { (x+3) ² }   you have to square first

and if it is     { 2 (x+3) }²    you have to multiply first



and it doesn't equal..........(2x+3)^2   and  2(x^2+6x+9)

and l don't get the last question you asked.

(if you explain more, I'll answer you as much as I can

Bye!

　

　

Answer 2

1. Because f(X) indicates that the equation is definitely a function. when its Y only, it might be only equation, it might be function as well. It also shows that x is variable and f(X) can have different values.

2. You square the values in brackets first, then multiply what you have received after squaring them : 2(x+3)*2= 2(x*2 + 6x+ 6)= 2x*2 + 12x +12

3. You would need to divide only if you had 2 on the Y side. Otherwise, you don't need to divide it.

Answer 3

1. f(x) is used to denote that "y is a function of x". In other words, the independent variable x is used to determine the value of y. Both just mean the same thing.

2. Your number 2 is correct.

3. Because in the original equation (x+a)^2 you will get x^2+2ax +a^2 so you divide the first degree literal coefficient by 2.

Answer 4

Now we are BOTH confused.

Answer 5

I'll answer the second point first

2(x+3)^2 is NOT (2x + 3)^2

It is 2(x^2 + 6x + 9)  

When completing the square you divide each term of the equation including the coefficient of 'x' by the coefficient of x^2 as follows:

ax^2 + bx +c = 0

x^2 + (b/a)x + c/a = 0

Next write x^2 + (b/a)x     =  - c/a

Now add (b^2)/(4a^2) to both sides which you are entitled to do without making the equation untrue.

You now have

x^2 + (b/a)x + (b^2)/(4a^2) = (b^2)/(4a^2) - c/a

The left hand side is

[x + (b/2a)]^2  and is equal to [b^2 - 4ac]/4a^2  on the right hand side

Take the square root on each side and

x + (b/2a) = [sqrt(b^2 - 4ac)]/2a

Therefore x = [-b +/-sqrt(b^2 - 4ac)]/2a  

Actually you are setting the thing up so that it becomes a perfect square on the left hand side keeping in mind that

(a+b)^2 = a^2+2ab+b^2 .

As to the first point the answer is basically yes f(x) is y but sometimes is it more expressive in that we can use f(a) to indicate the value of the function when x = a  if you like the value of y when x = a

It is a notation which is useful frequently. Get used to it.